Fuel supplier selection for large scale UK bioenergy schemes

This article presents a potential method to assist developers of future bioenergy schemes when selecting from available suppliers of biomass materials. The method aims to allow tacit requirements made on biomass suppliers to be considered at the design stage of new developments. The method used is a combination of the Analytical Hierarchy Process and the Quality Function Deployment methods (AHP-QFD). The output of the method is a ranking and relative weighting of the available suppliers which could be used to improve optimization algorithms such as linear and goal programming. The paper is at a conceptual stage and no results have been obtained. The aim is to use the AHP-QFD method to bridge the gap between treatment of explicit and tacit requirements of bioenergy schemes; allowing decision makers to identify the most successful supply strategy available.

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Distributed algorithms for global optimization on sparse networks of arbitrary bandwidths

The optimization of resource allocation in sparse networks with real variables is studied using methods of statistical physics. Efficient distributed algorithms are devised on the basis of insight gained from the analysis and are examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.

Modelling the dynamics of genetic algorithms using statistical mechanics

A formalism for modelling the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics, originally due to Prugel-Bennett and Shapiro, is reviewed, generalized and improved upon. This formalism can be used to predict the averaged trajectory of macroscopic statistics describing the GA's population. These macroscopics are chosen to average well between runs, so that fluctuations from mean behaviour can often be neglected. Where necessary, non-trivial terms are determined by assuming maximum entropy with constraints on known macroscopics. Problems of realistic size are described in compact form and finite population effects are included, often proving to be of fundamental importance. The macroscopics used here are cumulants of an appropriate quantity within the population and the mean correlation (Hamming distance) within the population. Including the correlation as an explicit macroscopic provides a significant improvement over the original formulation. The formalism is applied to a number of simple optimization problems in order to determine its predictive power and to gain insight into GA dynamics. Problems which are most amenable to analysis come from the class where alleles within the genotype contribute additively to the phenotype. This class can be treated with some generality, including problems with inhomogeneous contributions from each site, non-linear or noisy fitness measures, simple diploid representations and temporally varying fitness. The results can also be applied to a simple learning problem, generalization in a binary perceptron, and a limit is identified for which the optimal training batch size can be determined for this problem. The theory is compared to averaged results from a real GA in each case, showing excellent agreement if the maximum entropy principle holds. Some situations where this approximation brakes down are identified. In order to fully test the formalism, an attempt is made on the strong sc np-hard problem of storing random patterns in a binary perceptron. Here, the relationship between the genotype and phenotype (training error) is strongly non-linear. Mutation is modelled under the assumption that perceptron configurations are typical of perceptrons with a given training error. Unfortunately, this assumption does not provide a good approximation in general. It is conjectured that perceptron configurations would have to be constrained by other statistics in order to accurately model mutation for this problem. Issues arising from this study are discussed in conclusion and some possible areas of further research are outlined.

Optimization of PCB component placements for the collect-and-place machines

This paper presents two hybrid genetic algorithms (HGAs) to optimize the component placement operation for the collect-and-place machines in printed circuit board (PCB) assembly. The component placement problem is to optimize (i) the assignment of components to a movable revolver head or assembly tour, (ii) the sequence of component placements on a stationary PCB in each tour, and (iii) the arrangement of component types to stationary feeders simultaneously. The objective of the problem is to minimize the total traveling time spent by the revolver head for assembling all components on the PCB. The major difference between the HGAs is that the initial solutions are generated randomly in HGA1. The Clarke and Wright saving method, the nearest neighbor heuristic, and the neighborhood frequency heuristic are incorporated into HGA2 for the initialization procedure. A computational study is carried out to compare the algorithms with different population sizes. It is proved that the performance of HGA2 is superior to HGA1 in terms of the total assembly time.

Inference and optimization of real edges on sparse graphs:A statistical physics perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory. © 2007 The American Physical Society.

Exploring ant-based algorithms for gene expression data analysis

Objective: Recently, much research has been proposed using nature inspired algorithms to perform complex machine learning tasks. Ant colony optimization (ACO) is one such algorithm based on swarm intelligence and is derived from a model inspired by the collective foraging behavior of ants. Taking advantage of the ACO in traits such as self-organization and robustness, this paper investigates ant-based algorithms for gene expression data clustering and associative classification. Methods and material: An ant-based clustering (Ant-C) and an ant-based association rule mining (Ant-ARM) algorithms are proposed for gene expression data analysis. The proposed algorithms make use of the natural behavior of ants such as cooperation and adaptation to allow for a flexible robust search for a good candidate solution. Results: Ant-C has been tested on the three datasets selected from the Stanford Genomic Resource Database and achieved relatively high accuracy compared to other classical clustering methods. Ant-ARM has been tested on the acute lymphoblastic leukemia (ALL)/acute myeloid leukemia (AML) dataset and generated about 30 classification rules with high accuracy. Conclusions: Ant-C can generate optimal number of clusters without incorporating any other algorithms such as K-means or agglomerative hierarchical clustering. For associative classification, while a few of the well-known algorithms such as Apriori, FP-growth and Magnum Opus are unable to mine any association rules from the ALL/AML dataset within a reasonable period of time, Ant-ARM is able to extract associative classification rules.

Structural optimization

The non-linear programming algorithms for the minimum weight design of structural frames are presented in this thesis. The first, which is applied to rigidly jointed and pin jointed plane frames subject to deflexion constraints, consists of a search in a feasible design space. Successive trial designs are developed so that the feasibility and the optimality of the designs are improved simultaneously. It is found that this method is restricted lo the design of structures with few unknown variables. The second non-linear programming algorithm is presented .in a general form. This consists of two types of search, one improving feasibility and the other optimality. The method speeds up the 'feasible direction' approach by obtaining a constant weight direction vector that is influenced by dominating constraints. For pin jointed plane and space frames this method is used to obtain a 'minimum weight' design which satisfies restrictions on stresses and deflexions. The matrix force method enables the design requirements to be expressed in a general form and the design problem is automatically formulated within the computer. Examples are given to explain the method and the design criteria are extended to include member buckling. Fundamental theorems are proposed and proved to confirm that structures are inter-related. These theorems are applicable to linear elastic structures and facilitate the prediction of the behaviour of one structure from the results of analysing another, more general, or related structure. It becomes possible to evaluate the significance of each member in the behaviour of a structure and the problem of minimum weight design is extended to include shape. A method is proposed to design structures of optimum shape with stress and deflexion limitations. Finally a detailed investigation is carried out into the design of structures to study the factors that influence their shape.

Message-passing for inference and optimization of real variables on sparse graphs

The inference and optimization in sparse graphs with real variables is studied using methods of statistical mechanics. Efficient distributed algorithms for the resource allocation problem are devised. Numerical simulations show excellent performance and full agreement with the theoretical results. © Springer-Verlag Berlin Heidelberg 2006.

What are dynamic optimization problems?

Dynamic Optimization Problems (DOPs) have been widely studied using Evolutionary Algorithms (EAs). Yet, a clear and rigorous definition of DOPs is lacking in the Evolutionary Dynamic Optimization (EDO) community. In this paper, we propose a unified definition of DOPs based on the idea of multiple-decision-making discussed in the Reinforcement Learning (RL) community. We draw a connection between EDO and RL by arguing that both of them are studying DOPs according to our definition of DOPs. We point out that existing EDO or RL research has been mainly focused on some types of DOPs. A conceptualized benchmark problem, which is aimed at the systematic study of various DOPs, is then developed. Some interesting experimental studies on the benchmark reveal that EDO and RL methods are specialized in certain types of DOPs and more importantly new algorithms for DOPs can be developed by combining the strength of both EDO and RL methods.

Efficient algorithm for routing optimization via statistical mechanics

Many practical routing algorithms are heuristic, adhoc and centralized, rendering generic and optimal path configurations difficult to obtain. Here we study a scenario whereby selected nodes in a given network communicate with fixed routers and employ statistical physics methods to obtain optimal routing solutions subject to a generic cost. A distributive message-passing algorithm capable of optimizing the path configuration in real instances is devised, based on the analytical derivation, and is greatly simplified by expanding the cost function around the optimized flow. Good algorithmic convergence is observed in most of the parameter regimes. By applying the algorithm, we study and compare the pros and cons of balanced traffic configurations to that of consolidated traffic, which provides important implications to practical communication and transportation networks. Interesting macroscopic phenomena are observed from the optimized states as an interplay between the communication density and the cost functions used. © 2013 IEEE.

Distributed optimization in transportation and logistics networks

Many important problems in communication networks, transportation networks, and logistics networks are solved by the minimization of cost functions. In general, these can be complex optimization problems involving many variables. However, physicists noted that in a network, a node variable (such as the amount of resources of the nodes) is connected to a set of link variables (such as the flow connecting the node), and similarly each link variable is connected to a number of (usually two) node variables. This enables one to break the problem into local components, often arriving at distributive algorithms to solve the problems. Compared with centralized algorithms, distributed algorithms have the advantages of lower computational complexity, and lower communication overhead. Since they have a faster response to local changes of the environment, they are especially useful for networks with evolving conditions. This review will cover message-passing algorithms in applications such as resource allocation, transportation networks, facility location, traffic routing, and stability of power grids.